Pour 2 cups sugar into the center of a deep saucepan. Carefully pour the water around the sugar, trying not to splash any sugar onto the sides of the pan. Do not stir; gently draw your finger through the center of the sugar twice, making a cross, to moisten it. Over medium-high heat, bring to a boil without stirring. Reduce the heat to a fast simmer and cook without stirring until amber-caramel in color, 10 to 20 minutes. Immediately remove from the heat. Meanwhile, set 6 (1-cup ramekins or shallow coffee cups nearby. When the caramel is cooked, quickly pour about 1/4 cup caramel into each ramekin and swirl to coat the sides. Set aside to cool.
In a saucepan, bring the milk and vanilla bean to a boil over medium heat. Immediately turn off the heat and set aside to infuse. Meanwhile, in a large bowl, whisk together the eggs, additional egg yolks and the remaining 1 cup sugar. Whisk about 1/2 cup of the hot milk into the egg mixture. Whisk the remaining hot milk into the egg mixture. Whisk in the mango puree until smooth. Strain the mixture into a pitcher to smooth it and to remove the vanilla bean and mango fibers. Pour the mixture into the caramel-lined ramekins and arrange in a hot water bath. Bake in the center of the oven until dry and set in the center, 30 to 35 minutes. Remove from the water bath and let cool. Tightly cover each ramekin with plastic wrap. Refrigerate at least 2 hours, or refrigerate until ready to serve, up to 24 hours.
To serve, place a brownie circle on each serving plate. Turn a flan out on top of the cake (you may need to dip the bottom of each ramekin in hot water to loosen the caramel, and/or run a knife around the edge of the ramekin). The caramel will pour out and serve as the sauce, and will also soak into the brownie.
Chocolate Brownie Base:
Preheat the oven to 350 degrees. Grease a 9 by 13-inch baking pan and line it with parchment or waxed paper, pressing into the corners. In a mixer fitted with a paddle attachment (or using a hand mixer), cream the butter until fluffy. Mix in the sugar. Mix in the eggs and vanilla and mix until light and fluffy. Sift together the flour, cocoa powder, baking soda and salt. Add to the butter mixture and mix just until combined. Mix in the chocolate chips. Pour into the prepared pan, smooth the top, and bake until the cake is firm in the center and the surface is dry and shiny, 15 minutes. Let cool in the pan. Run a knife around the edges of the pan and turn out the whole cake onto a work surface. Peel off the waxed paper. Using a ramekin as a guide, use a sharp knife to cut out 6 brownie circles the same size as the ramekins.
Courtesy Gale Gand, "Butter Sugar Flour Eggs" by Gale Gand, Rick Tramonto, Julia Moskin, Clarkson N. Potter Publishers, 1999